Computational and neural mechanisms of statistical pain learning

Pain invariably changes over time. These fluctuations contain statistical regularities which, in theory, could be learned by the brain to generate expectations and control responses. We demonstrate that humans learn to extract these regularities and explicitly predict the likelihood of forthcoming pain intensities in a manner consistent with optimal Bayesian inference with dynamic update of beliefs. Healthy participants received probabilistic, volatile sequences of low and high-intensity electrical stimuli to the hand during brain fMRI. The inferred frequency of pain correlated with activity in sensorimotor cortical regions and dorsal striatum, whereas the uncertainty of these inferences was encoded in the right superior parietal cortex. Unexpected changes in stimulus frequencies drove the update of internal models by engaging premotor, prefrontal and posterior parietal regions. This study extends our understanding of sensory processing of pain to include the generation of Bayesian internal models of the temporal statistics of pain.

To inspect the quality of fit of the winning model (Bayesian jump frequency model), we evaluated the relation between the frequency p(H) predicted by the Bayesian jump frequency model vs. individual participants (one regression line for each participant in Supplementary Figure 1). At group level, the correlation coefficients were significantly above 0 (r=0.829, t(35)=8.629, p<0.001, two-sided statistics).

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We evaluated, in each participant, the correlation between the high pain rating (averaged across blocks) and the prediction accuracy (measured by the correlation coefficient between rated and true frequencies and transition probabilities). There was no evidence for a correlation between mean pain intensity and prediction accuracy (frequency prediction accuracy by high pain intensity: r = -0.175, p = 0.337; p(H|H) prediction accuracy by high pain intensity: r = -0.178, p = 0.305; 2).

Supplementary Figure 2.
Mean intensity of high stimulus by prediction accuracy for frequencies (a) and transition probabilities (b). .

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Cluster

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We conducted three separate fMRI analyses, each adding a different covariate to the generalised linear mixed model presented in the main article (regressors of interest: posterior mean p(high), SD posterior, KL divergence, stimulus intensity). The covariates we tested were: (1) the evidence of the Bayesian jump frequency model; (2) the prediction accuracy, as indexed by the coefficient of the correlation between the transition probability p(L|H) rated by the subject and the true p(L|H); (3) an alternative measure of prediction accuracy, i.e. the coefficient of the correlation between the stimulus frequency predicted by the subject vs. the Bayesian jump frequency model.
The neural correlates of the mean posterior of low/high pain (probabilistic inference), model update and posterior SD (uncertainty of the inference) were very similar across the different control analyses we conducted (figures 4, 5, 6), and also remarkably similar to those reported in the main article (figures 9-12).  Figure 6. Neural correlates of the (a) mean posterior of low (green) and high (pink) pain frequency, (b) update of the Bayesian jump frequency model, and (c) uncertainty after controlling for an alternative measure of prediction accuracy (i.e., the correlation between the frequency of low pain rated by the subject and predicted by the Bayesian jump frequency model.

Supplementary
Our model fitting and comparison analyses indicate that participants in our sample used a Bayesian inference strategy with dynamic update of beliefs, but there were inter-individual differences in the nature of temporal statistics inferred. Whereas 23 participants favoured the inference of the frequency of the stimuli, 12 participants preferred to infer the transition probability (TP) of the stimuli, which yields more accurate predictions. Thus, we conducted additional followup neuroimaging analyses to explore these group differences.
First, we divided participants in two groups, according to their preferred inference strategy, defined as the model with the highest evidence (frequency: n=23, TP: n=12). For each subject, we derived the mean posterior inference, SD posterior and model update (KL divergence between two consecutive posterior distributions) in the jump frequency model and in the jump TP model. After convolving them with a hemodynamic response function, we used them as trial-by-trial regressors for BOLD responses, on each individual, separately for the two models. We then contrasted neural correlates of inference, uncertainty and model update between the two groups (preferred learning strategy: frequency vs. TP), separately for each model (Bayesian jump frequency vs. TP).
We found no significant group differences in the neural correlates of predictive inference (mean posterior of stimulus frequency) and uncertainty (SD posterior of stimulus frequency) in either model. However, the update of the jump frequency and TP models (KL divergence) was associated with increased activity in the left orbitofrontal cortex in the group that favoured frequency inference than in the group that favoured TP inference (jump frequency model: peak x -24, y 28, z -16, z-stat 4.806; jump TP model: peak x -26, y 25, z -19, z-stat 4.504; Supplementary  Figure 7). Figure 7. The left orbitofrontal cortex was more active in the group of participants that favoured a frequency inference strategy over a transition probability strategy, in association with the update of the jump frequency (a) and transition probability models (b).